The practice of scientific modelling often resorts to hypothetical, false, idealised, targetless, partial, generalised, and other types of modelling that appear to have at least partially non-actual targets. In this paper, I will argue that we can avoid a commitment to non-actual targets by sketching a framework where models are understood as having networks of possibilities as their targets. This raises a further question: what are the truthmakers for the modal claims that we can derive from models? I propose that (...) we can find truthmakers for the modal claims derived from models in actuality, even in the case of supposedly non-actual targets. I then put this framework to use by examining a case study concerning the modelling of superheavy elements. (shrink)

In this paper, I discuss how to distinguish between ontological categories and ordinary categories. Using an argument against van Inwagen’s proposed account of what makes a category ontological as a springboard, I argue that if ontological categories are modally robust, then ontological categories need to be understood hyperintensionally. This conclusion opens up a wide range of new ways to define ‘ontological category’, and I close by briefly outlining one such way in order to illustrate the advantages of embracing hyperintensionality in (...) this debate. (Published Open Access). (shrink)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

I know that I could have been where you are right now and that you could have been where I am right now, but that neither of us could have been turnips or natural numbers. This knowledge of metaphysical modality stands in need of explanation. I will offer an account based on our knowledge of the natures, or essencess, of things. I will argue that essences need not be viewed as metaphysically bizarre entities; that we can conceptualise and refer to (...) essences; and that we can gain knowledge of them. We can know about which properties are, and which properties are not, essential to a given entity. This knowledge of essence offers a route to knowledge of the ways those entities must be or could be. (shrink)

In this paper, I raise the problem of dealing with counterpossible conditionals for theories of subject matter. I argue that existing accounts of subject matter need to be revised and extended to be able to a) provide reasonable (potentially non-degenerate) verdicts about what counterpossibles are about, b) explain the intuition that counterpossibles are in some sense about what would happen if the antecedent were true, and c) explain in what sense counterpossibles can be about individuals. I sketch how one could (...) extend atom-based and way-based theories of subject matters to handle the problem. Then, I raise the problem that it might be desirable for a theory of subject matter to prevent the inference that certain counterpossibles are about the kinds of things that they seem to mention. (shrink)

It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...) antecedents at some world, the same worlds are deemed as relevant for all occasions of utterance. But surely this is inadequate, if shifts of contexts between occasions are to be accounted for. Both the linguistic and logical implications of this defect are discussed, and in order to overcome it a modification of David Lewis’ ordering semantics for counterfactuals is developed for a modified language. I follow Lewis by letting contexts determine comparative similarity assignments, and show that the addition of syntactic context parameters (context indices) to the language gives the freedom required to switch between sets of relevant antecedent worlds from occasion to occasion by choosing the corresponding similarity assignment accordingly. Thus an account that extends Lewis’ analysis of a language containing a single counterfactual connective > to a language containing infinitely many counterfactual connectives >_c, each indexed by a different context name c, overcomes the limitations of traditional analyses. Finally it is also shown that these traditional accounts can be recovered from the modified account if certain contextual restrictions are in place. -/- . (shrink)

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

It has been suggested that intuitions supporting the nonvacuity of counterpossibles can be explained by distinguishing an epistemic and a metaphysical reading of counterfactuals. Such an explanation must answer why we tend to neglect the distinction of the two readings. By way of an answer, I offer a generalized pattern for explaining nonvacuity intuitions by a stand-and-fall relationship to certain indicative conditionals. Then, I present reasons for doubting the proposal: nonvacuists can use the epistemic reading to turn the table against (...) vacuists, telling apart significant from spurious intuitions. Moreover, our intuitions tend to survive even if we clear-headedly intend a metaphysical reading. -/- . (shrink)

There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how these investigations (...) help to clarify the role that expressive power plays within debates in metaphysics, logic, and the philosophy of language. (shrink)

According to classical theism, the universe depends on God in a way that goes beyond mere (efficient) causation. I have previously argued that this ‘deep dependence’ of the universe on God is best understood as a type of grounding. In a recent paper in this journal, Aaron Segal argues that this doctrine of deep dependence causes problems for creaturely free will: if our choices are grounded in facts about God, and we have no control over these facts, then we do (...) not control our choices and are therefore not free. This amounts to a grounding analogue of the Consequence Argument for the incompatibility of free will and determinism. If successful, it would have application beyond classical theism: similar concerns would apply to any view that takes our choices to be grounded in a deeper reality which is beyond our control. However, I show that the argument is not successful. Segal’s Grounding Consequence Argument is so closely analogous to the Causal Consequence Argument that any response to the one provides a response to the other. As a result, if you don’t think that prior causes (whether deterministic or indeterministic) undermine free will, you shouldn’t think that prior grounds undermine free will. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...) interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. (shrink)

If ontic dependence is the basis of explanation, there cannot be mathematical explanations. Accounting for the explanatory dependency between mathematical properties and empirical phenomena poses i...

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such (...) an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain. (shrink)

Spinoza reasons about impossibilities on a regular basis. But he also says they're unthinkable and that reasoning is a mental process. How can he do this? The paper defends a linguistic account of counterpossible inferences in Spinoza's geometrical method.

Counterpossibles, counterfactuals conditional with impossible antecedents, are notoriously contested; while the standard view makes them trivially true, some authors argue that they can be non-trivially true. In this paper, I examine the use of counterfactuals in the context of games, and argue that there is a case to be made for their non-triviality in a restricted sense. In particular, I examine the case of retro problems in chess, where it can happen that one is tasked with evaluating counterfactuals about illegal (...) positions. If we understand illegality as a type of restricted impossibility, those counterfactuals are non-trivial counterpossibles. I suggest that their non-triviality stems from their role in practices of rule coordination and revision, and suggest that this model could be generalized to counterpossibles in different domains. I then compare the approach to the accounts of Vetter 2016 and Locke 2019. (shrink)

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (shrink)

An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically indeterminate whether (...) p just in case it is neither true nor false that p, and no terms in ‘p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent. (shrink)

I discuss several problems for Williamson’s counterfactual-theory of modal knowledge and argue that they have a common source, in that the theory neglects to elucidate the proper constraints on modal reasoning. Williamson puts forward an empirical hypothesis that rests on the role of counterfactual reasoning for modal knowledge. But he overlooks central questions of normative modal epistemology. In order for counterfactual reasoning to yield correct beliefs about modality, it needs to be suitably constrained. I argue that what is needed is, (...) specifically, information concerning the nature or essence of things. By integrating this information, essentialist deduction arguably provides a better account of our knowledge of modality. Furthermore, I argue that essences have distinctive causal and explanatory powers—indeed, essences are superexplanatory for how things are. Compared to Williamson’s counterfactual-theory, superexplanatory essentialism clarifies what the proper constraints on modal reasoning are, and why they have such a special status. (shrink)

Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan, on which we also (...) consider impossible worlds. Nolan’s account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S’s belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities. (shrink)

Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...) a counterfactual is explanatory when it is an instance of a generalized counterfactual scheme. (shrink)

Recently, a debate has developed between those who claim that essence can be explained in terms of de re modality (modalists), and those who claim that de re modality can be explained in terms of essence (essentialists). The aim of this paper is to suggest that we should reassess. It is assumed that either necessity is to be accounted for in terms of essence, or that essence is to be accounted for in terms of necessity. I will argue that we (...) should assume neither. I discuss what role these key notions – essence and necessity – can reasonably be thought to contribute to our understanding of the world, and argue that, given these roles, there is no good reason to think that we should give an account of one in terms of the other. I conclude: if we can adequately explain de re modality and essence at all, we should aim to do so separately. (shrink)

In my thesis, I aim to develop a systematic and philosophically coherent thesis of ultimate reality for Ibn Arabi. In this pursuit, I adopt the style of analytic philosophy, seeking to employ and utilise some of its methods and theories. The philosophical aspects of Ibn Arabi’s doctrine are in dire need of conceptual clarification and systematic analysis with a closer focus on argumentation. The analytic tradition will prove most helpful in this regard. In my thesis, I begin by tracing Ibn (...) Arabi’s related views and concepts as they are dispersed throughout his writings. I then clarify, sharpen and, in many cases, develop these views and concepts into fully constructed forms. Finally, I weave the developed concepts and views into a systematic thesis or set of sub-theses. Where necessary, I provide my own arguments and concepts to help substantiate and strengthen the structure of Ibn Arabi’s thesis. I propose that Ibn Arabi’s various, and sometimes apparently inconsistent, views are best presented in terms of three main concepts: the concept of ultimate reality as existence, which has long been known as Ibn Arabi’s thesis of the oneness of existence ; the concept of ultimate reality as the Divine Self ; and the concept of ultimate reality as God. The three concepts neither represent different ultimate realities nor different perspectives of the same ultimate reality. Instead, they represent the same ultimate reality but each one has its own unique scope and encompassment. The three concepts are aimed at encompassing Ibn Arabi’s various views and concepts of ultimate reality in a consistent and systematic manner. (shrink)

The will of an omnipotent being would be perfectly efficacious. Alexander Pruss and I have provided an analysis of perfect efficacy that relies on non-trivial counterpossible conditionals. Scott Hill has objected that not all of the required counterpossibles are true of God. Sarah Adams has objected that perfect efficacy of will (on any analysis) would be an extrinsic property and so is not suitable as a divine attribute. I argue that both of these objections can be answered if the divine (...) will is taken to be the ground, rather than the cause, of its fulfillment. (shrink)

According to proponents of the causal exclusion problem, there cannot be a sufficient physical cause and a distinct mental cause of the same piece of behaviour. Increasingly, the causal exclusion problem is circumvented via this compatibilist reasoning: a sufficient physical cause of the behavioural effect necessitates the mental cause of the behavioural effect, so the effect has a sufficient physical cause and a mental cause as well. In this paper, I argue that this compatibilist reply fails to resolve the causal (...) exclusion problem. (shrink)

This paper argues that modal realism has a problem with mathematical impossibilities. Due to the peculiar way it treats both propositions and mathematical objects, modal realism cannot distinguish the content of different mathematically impossible beliefs. While one might be happy to identify all logically impossible beliefs, there are many different mathematically impossible beliefs, none of which is a belief in a logical contradiction. The fact that it cannot distinguish these beliefs speaks against adopting modal realism.

According to Michael Almeida, reflections on free will and possibility can be used to show that the existence of an Anselmian God is compatible with the existence of evil. These arguments depend on the assumption that an agent can be free with respect to an action only if it is possible that that agent performs that action. Although this principle enjoys some intuitive support, I argue that Anselmianism undermines these intuitions by introducing impossible options. If Anselmianism is true, I argue, (...) then both God and creatures may be free to do the impossible. (shrink)

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing on lessons from (...) these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

Substantive counterlegal discourse poses a problem for those according to whom the laws of nature are metaphysically necessary. I discern two types of necessitarianism about laws: dispositional essentialism and modal necessitarianism. I argue that Toby Handfield’s response to the problem of counterlegals cannot help the modal necessitarian, according to whom all possible worlds are identical with respect to the laws. I thus propose a fictionalist treatment of counterlegals. Fictions are not limited by metaphysical possibility; hence, fictionalism affords the modal necessitarian (...) the means to account for the apparent substance of counterlegals even granting the metaphysical necessity of the laws. (shrink)

The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While certain (...) of the latter systems are shown to have similar problems to logics from the first approach, at least one relatively weak system appears to offer an adequate uniform semantics for counterpossibles and counterfactuals. (shrink)

It is a truth universally acknowledged that a claim of metaphysical modality, in possession of good alethic standing, must be in want of an essentialist foundation. Or at least so say the advocates of the reductive-essence-first view, according to which all modality is to be reductively defined in terms of essence. Here, I contest this bit of current wisdom. In particular, I offer two puzzles—one concerning the essences of non-compossible, complementary entities, and a second involving entities whose essences are modally (...) ‘loaded’—that together strongly call into question the possibility of reducing modality to essence. (shrink)

In a recent issue of this journal, Berit Brogaard and Joe Salerno presented a counterfactual theory of essence, designed to get around Kit Fine’s influential objections to the standard modal account of essence. I argue that Brogaard and Salerno’s theory does not avoid Fine’s objections. Then I propose a sequence of variations on their theory, and argue that none of them succeed either.

Metaethical debunking arguments often conclude that no moral belief is epistemically justified. Early versions of such arguments largely relied on metaphors and analogies and left the epistemology of debunking underspecified. Debunkers have since come to take on substantial and broad-ranging epistemological commitments. The plausibility of metaethical debunking has thereby become entangled in thorny epistemological issues. In this thesis, I provide a critical yet sympathetic evaluation of the prospects and challenges facing such arguments in light of this development. In doing so, (...) I address the following central question: how could genealogical information undermine the epistemic justification of moral beliefs? In Part I, I begin answering the central question by extracting explicit and implicit epistemic principles from three popular debunking arguments. These arguments, due to Gilbert Harman, Richard Joyce, and Sharon Street, generate principles concerning ontological parsimony, explanatory dispensability, epistemic insensitivity, lack of epistemic safety, unexplained reliability, epistemic coincidences, and explanatory constraints on rational belief. Having set out the principles tasked with explaining how genealogical information undermines, Part II of the thesis seeks to evaluate whether debunking arguments built on them succeed. To this end, I consider two types of challenges faced by such arguments. First, there are strategies that attempt to block global moral debunking arguments. I argue that one popular such strategy, the so-called ‘third-factor strategy’, has been misunderstood. When understood correctly, it is of no help in answering debunking arguments. I then flesh out an alternative and more promising strategy for blocking such arguments. I then turn to internal challenges facing debunkers, particularly those who rely on ‘explanationist’ principles. I argue that explanationist debunking arguments, as well as most others, fall prey to one or more of four internal challenges: the implausibility of first-order epistemic principles, the threat of overgeneralization, the threat of self-defeat, and the need for costly metaepistemic commitments. I conclude that current debunking arguments fail to establish that no moral belief is justified. By analyzing why existing arguments fail, I develop two conditions of adequacy that debunkers must satisfy in order to navigate the internal challenges successfully. I end by suggesting future directions that debunkers should pursue to rehabilitate the prospects for global moral debunking arguments. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

According to sparse modalism, the notion of essence can be analysed in terms of necessity and naturalness. In this paper, I develop and defend a version of sparse modalism that is equipped with a non-standard, relativized conception of naturalness. According to this conception, properties and relations can be natural to different degrees relative to different kinds of things, and relations can be natural to different degrees relative to different slots. I argue that this relativized version of sparse modalism can accommodate (...) various cases that the standard, non-relativized version can’t. The alternative version can accommodate cases where a relation is essential to a relatum but merely necessary to another, cases where a property is essential to an object but merely necessary to another, and cases where a less-than-perfectly natural property is essential to an object. (shrink)

This paper deals with generalisations of modally based criteria for determining whether a given property is essential to an individual to the case of generic essences. These criteria usually presuppose extensionally individuated properties. The limitations of their generalisations are demonstrated using the case of the necessarily empty individual property and the necessarily empty individual office. I do not present a novel stance on the discussion of individual essences. The novelty of this paper lies in its claim that none of these (...) criteria can be generalised to generic essences. (shrink)

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)

It is a truth universally acknowledged that a claim of metaphysical modality, in possession of good alethic standing, must be in want of an essentialist foundation. Or at least so say the advocates of thereductive-essence-firstview, according to which all modality is to be reductively defined in terms of essence. Here, I contest this bit of current wisdom. In particular, I offer two puzzles—one concerning the essences of non-compossible, complementary entities, and a second involving entities whose essences are modally ‘loaded’—that together (...) strongly call into question the possibility of reducing modality to essence. (shrink)

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne, who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening, which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close (...) by discussing the dispensability of counterfactual conditionals within the language of mathematics. (shrink)

What is it for something to be essential to an item? For some time, it was standard to think that the concept of necessity alone can provide an answer: for something to be essential to an item is for it to be strictly implied by the existence of that item. We now tend to think that this view fails because its analysans is insufficient for its analysandum. In response, some argue that we can supplement the analysis in terms of necessity (...) with a further condition. In this paper I argue that this view is untenable in its current form. I then provide a glimmer of hope to those who think that essence is at least partially analyzable in terms of necessity. (shrink)

This article examines three candidate cases of non-causal explanation in computational neuroscience. I argue that there are instances of efficient coding explanation that are strongly analogous to examples of non-causal explanation in physics and biology, as presented by Batterman, Woodward, and Lange. By integrating Lange’s and Woodward’s accounts, I offer a new way to elucidate the distinction between causal and non-causal explanation, and to address concerns about the explanatory sufficiency of non-mechanistic models in neuroscience. I also use this framework to (...) shed light on the dispute over the interpretation of dynamical models of the brain. _1_ Introduction _1.1_ Efficient coding explanation in computational neuroscience _1.2_ Defining non-causal explanation _2_ Case I: Hybrid Computation _3_ Case II: The Gabor Model Revisited _4_ Case III: A Dynamical Model of Prefrontal Cortex _4.1_ A new explanation of context-dependent computation _4.2_ Causal or non-causal? _5_ Causal and Non-causal: Does the Difference Matter? (shrink)

Making sense of our reasoning in disputes about necessary truths requires admitting nonvacuous counterpossibles. One class of these is the counteressentials, which ask us to make contrary to fact suppositions about essences. A popular strategy in accounting for nonvacuous counterpossibles is to extend the standard possible worlds semantics for subjunctive conditionals by the addition of impossible worlds. A conditional A □-> C is then taken to be true if all of the nearest A worlds are C worlds. I argue that (...) a straightforward extension of the standard possible worlds semantics to impossible worlds does not result in a viable account of counteressentials and propose an alternative covering law semantics for counteressentials. (shrink)

Widespread causal overdetermination is often levied as an objection to nonreductive theories of minds and objects. In response, nonreductive metaphysicians have argued that the type of overdetermination generated by their theories is different from the sorts of coincidental cases involving multiple rock-throwers, and thus not problematic. This paper pushes back. I argue that attention to differences between types of overdetermination discharges very few explanatory burdens, and that overdetermination is a bigger problem for the nonreductive metaphysician than previously thought.